Equation of a Tangent to a Curve (Grade 12 NSC Matric Mathematics): Quizzes

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Equation of a Tangent to a Curve
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What is a tangent line to a curve?

A line touching the curve at exactly one point

At a point on a curve, what equals the gradient of the tangent?

The gradient of the curve at that point

What does the derivative of a function give us?

The gradient of the curve at any point

What is the first step in finding the equation of a tangent?

Find the derivative

What is the point-gradient form equation?

y−y1=m(x−x1)y - y_1 = m(x - x_1)

What is the relationship between perpendicular gradients?

mexttangent×mextnormal=−1m_{ ext{tangent}} \times m_{ ext{normal}} = -1

If the tangent gradient is 44, what is the normal gradient?

−14-\frac{1}{4}

For y=3x2y = 3x^2, what is dydx\frac{dy}{dx} at x=1x = 1?

66

What is a common mistake when finding tangent equations?

Forgetting to find the y-coordinate

What is a normal line?

A line perpendicular to the tangent

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